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2.2 Variables

2.2 Variables

If we had a pattern that went 0, 2, 4, 6, 8, 10. Instead of using one line, we can introduce 2 lines, such that we now have:

x 0 1 2 3 4 5
y 0 2 4 6 8 10

Instead of saying that the y-values (i.e. second row) is increasing by 2, we can say the y is twice what x is.

This is a lot more beneficial, because we know that if we assign x=20, y is double, or y=20*2=40

In the scenario that we didn’t know that y is twice x (i.e. y=2*x, or alternatively, y=2x), we would have had to extend the table much further to the right to find the correct answer, which is inefficient!

Another example:

x 0 1 2 3 4 5
y 1 3 5 7 9 11

Note this time, that even though the increment is by 2, it is NOT y=2x any more. Rather, it is y=2x+1. As above, if we know x=40, y=40(2)+1=81.

The above questions are therefore an example of “finding the formula”. Alternatively, there may be an instance where you have to insert in an x, to obtain a y.